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Erschienen in:
2016 | Supplement | Buchkapitel
Modelling Stochastic Correlation
verfasst von : Long Teng, Matthias Ehrhardt, Michael Günther
Erschienen in: Progress in Industrial Mathematics at ECMI 2014
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Abstract
It is well known that the correlation between financial products, financial institutions, e.g., plays an essential role in pricing and evaluation of derivatives. Using a constant or deterministic correlation may lead to correlation risk, since market observations give evidence that the correlation is hardly a deterministic quantity.
Here, the approach of Teng et al. (A versatile approach for stochastic correlation using hyperbolic functions. Preprint 13/14. University of Wuppertal, 2013) for modelling the correlation as a hyperbolic function of a stochastic process is generalized to derive stochastic correlation processes (SCP) from a hyperbolic transformation of the modified Ornstein-Uhlenbeck process. We determine a transition density function of this SCP in closed form which could be used easily to calibrate SCP models to historical data.
As an example we compute the price of a quantity adjusting option (Quanto) and discuss concisely the effect of considering stochastic correlation on pricing the Quanto.